The growing availability of financial and economic data has led to a need for econometric methods to analyze and model it. The papers in this Special Issue on Large Dimensional Models arise out of the invited presentations given in The Econometrics Journal Special Session on this topic at theRoyal Economic Society Annual Conference held 7-9 April 2014 at the University of Manchester. Professors Jianqing Fan and Marc Hallin each addressed different aspects of this difficult and multi-faceted problem. Their conference presentations can be viewed on http://live.wavecast.co/res-annual-conference/session/large-dimensional-models-econometrics-journal-special-session/
The article that accompanies the presentation “An overview of the estimation of large covariance and precision matrices” by Jianqing Fan, co-authored with Yuan Liao and Han Liu, provides a review of recent developments in the statistics and econometrics literatures on the estimation of covariance matrices and inverse covariance matrices, known as precision matrices. These matrices appear in a variety of economic problems, including factor analyses, portfolio decision problems, and undirected graph construction. This article reviews methods based on thresholding, penalized likelihood estimation, and a factor model-based approach, and discusses methods to ensure that the resulting covariance or precision matrix is positive definite in finite samples (not only asymptotically). Also covered are methods that are applicable to fat-tailed data, relaxing the common assumption of Gaussianity, which is important for potential applications to financial asset returns . To view the complete paper please visit http://onlinelibrary.wiley.com/doi/10.1111/ectj.12061/abstract
The paper accompanying the presentation “Generalized dynamic factor models and volatilities: recovering the market volatility shocks” by Marc Hallin, co-authored with Matteo Barigozzi, addresses a more specific problem in the area of high dimensional econometrics, namely that of decomposing asset return volatilities into a common market-wide component and an idiosyncratic component. There is much related work on this problem in the financial econometrics literature. However, most existing studies employ parametric models, while the analysis presented here is nonparametric. This allows the authors to draw conclusions that are more robust than those based on potentially mis-specified models. It is noteworthy that while the focus of this article is on a possible factor structure in asset return volatilities, the analysis explicitly considers the possibility that there is very likely to be a factor structure in asset returns and that this factor structure need not match the one, if present, in return volatilities. This article applies the procedure to daily returns on the constituents of the Standard & Poor 100 Index and finds evidence of a single factor in both returns and volatilities but with the explanatory power of the common factor much stronger for returns than for volatilities. To view the complete paper please visit http://onlinelibrary.wiley.com/doi/10.1111/ectj.12047/abstract
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